asymptote question

Find all vertical, horizontal, and oblique asymptotes, and state if the function has any holes.

My first step was to simplify:

and cancel

My answer is:
Vertical asymptote at x=3. Horizontal asymptote at y=1. I don't think there is an oblique asymptote, because the degree of the numerator and denominator are equal. I believe there is a hole at

Is this correct? I guess my main question is, because I cancelled, does that eliminate the vertical asymptote x=-2 and replace it with the hole mentioned above?

Find all vertical, horizontal, and oblique asymptotes, and state if the function has any holes.

My first step was to simplify:

and cancel

My answer is:
Vertical asymptote at x=3. Horizontal asymptote at y=1. I don't think there is an oblique asymptote, because the degree of the numerator and denominator are equal. I believe there is a hole at

Is this correct? I guess my main question is, because I cancelled, does that eliminate the vertical asymptote x=-2 and replace it with the hole mentioned above?